### Playing With Numbers

goals
A boy multiplied $987$ by a certain number and obtained $559981$ as his answer. If in the answer both $9$ are wrong and the other digits are correct, then the correct answer would be:
When a natural number $n$ is divided by $4$, the remainder is $3$. What is the remainder when $2n$ is divided by $4$?
Consider the following statements:
A number ${ a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 }{ a }_{ 5 }$ is divisible by $9$ if
1. ${ a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 3 }+{ a }_{ 4 }+{ a }_{ 5 }$ is divisible by $9$.
2. ${ a }_{ 1 }-{ a }_{ 2 }+{ a }_{ 3 }-{ a }_{ 4 }+{ a }_{ 5 }$ is divisible by $9$.
Which of the above statements is/are correct?
Using divisibility tests, determine which of the following numbers are divisible by $10$:
(a) $54450$ (b) $10800$ (c) $7138965$ (d) $7016930$ (e) $10101010$
$24 P$ leaves remainder $1$ if it is divided by $3$ and leaves remainder $2$ if it is divided by $5$.
Find the value of $P$